It can act as a catalyst, just like footwork can also act as a catalyst in any stroke. But angular and linear momentum are two different things, and your "piecewise linear" approximation of a circle as a series of chords is not relevant to it.

If you are saying that there is a huge difference between staying still and rotating your racket, and moving your upper body forward and leaning on the ball and rotating your racket, you are right.

Yes it can...but linear momentum (as you mentioned) is the movement of one's center of mass in a straight line AND can be expressed in any direction. Modern players use considerable linear momentum (in an open stance for instance) by loading against the ground and pushing up to augment the tremendous rotational cycle that creates racquet head speed.

At any rate, as I mentioned, linear momentum has little direct effect on racquet head speed, but it's contribution to angular speed can be significant..